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Arithmetic Operations of Intuitionistic Z-Numbers Using Horizontal Membership Functions

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Part of the Lecture Notes in Networks and Systems book series (LNNS,volume 457)

Abstract

An intuitionistic Z-number (IZN) is an integration of an intuitionistic fuzzy number with a Z-number. The IZN composes of two components; restriction and reliability components, which are represented by the membership and non-membership degrees to indicate the hesitancy. The objective of this paper is to propose new arithmetic operations of IZN using the horizontal membership functions, which are closely related the concept of the relative distance measure. For that reason, the addition, subtraction, multiplication and division on normal trapezoidal IZNs are considered. The proposed operations preserve the arithmetic operations over real numbers and the original IZN-based information, avoiding any significant loss of information. The implementation of the bandwidth method in deriving the operations has reduced the computational complexity on IZN. In the future, aggregation operators of IZN can be derived using the proposed arithmetic operations.

Keywords

  • Intuitionistic Z-number
  • Arithmetic operation
  • Horizontal membership function
  • Relative distance measure

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Acknowledgements

This research is supported by the Ministry of Higher Education Malaysia under Fundamental Research Grant Scheme FRGS/1/2019/STG06/UMP/02/9.

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Correspondence to Ku Muhammad Naim Ku Khalif .

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Nik Badrul Alam, N.M.F.H., Ku Khalif, K.M.N., Jaini, N.I. (2022). Arithmetic Operations of Intuitionistic Z-Numbers Using Horizontal Membership Functions. In: Ghazali, R., Mohd Nawi, N., Deris, M.M., Abawajy, J.H., Arbaiy, N. (eds) Recent Advances in Soft Computing and Data Mining. SCDM 2022. Lecture Notes in Networks and Systems, vol 457. Springer, Cham. https://doi.org/10.1007/978-3-031-00828-3_3

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